Linear Equations and Inequalities

Linear equations and inequalities are fundamental concepts in algebra, and they are also an important part of the SAT Math section. Linear equations represent straight lines on a graph and can be used to model many real-world situations, such as the growth of a population or the depreciation of an asset over time. Inequalities, on the other hand, represent a range of possible values and are often used to express constraints or limitations in a given situation.

On the SAT, linear equations and inequalities are tested in a variety of ways, including solving equations for a given variable, graphing equations and inequalities, and using equations to solve word problems. By mastering these concepts, you'll be better equipped to tackle the SAT Math section and succeed in your college admissions journey.

To help you prepare for the SAT Math section, we've created a practice test for linear equations and inequalities. This test will give you the opportunity to practice solving problems similar to those you'll encounter on the SAT. As always, should you have any trouble with the questions on this test, don't hesitate to reach out for personalized SAT tutoring to help you ace this section. 

Good luck!

1. Solve for x:

3x - 7 = 8

1. 3

2. 4

3. 5

4. 6

2. Solve for y:

2y + 5 = 15

1. 2

2. 3

3. 4

4. 5

3. Solve the inequality:

-3x + 4 > 10

1. x < -2

2. x > -2

3. x < 2

4. x > 2

4. Solve the inequality:

4 - 5y ≤ 19

1. y ≤ -3

2. y ≥ -3

3. y ≤ 3

4. y ≥ 3

5. Solve the system of linear equations:

x + y = 5

2x - y = 1

1. (2, 3)

2. (1, 4)

3. (3, 2)

4. (4, 1)

6. Which of the following is the graph of the equation y = -2x + 3?

1. A line with a positive slope

2. A line with a negative slope

3. A horizontal line

4. A vertical line

7. What is the slope of the line represented by the equation 3x - 4y = 12?

1. 3/4

2. -3/4

3. 4/3

4. -4/3

8. Solve the inequality:

2x - 3 ≤ 3x + 2

1. x ≥ -5

2. x ≤ -5

3. x ≥ 5

4. x ≤ 5

9. What is the y-intercept of the line represented by the equation 6x - 3y = 9?

1. -3

2. 3

3. -2

4. 2

10. Solve the system of linear inequalities:

x + y > 4

x - 2y ≤ 6

1. x > 4, y > 0

2. x > 2, y < 3

3. x ≤ 4, y > 0

4. x ≤ 2, y < 3

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Try our other test papers:

1. Systems of Linear Equations & Inequalities
2. Interpretation of Linear Functions in Context